State estimation is one of the essential tasks for autonomous systems, which is required in multiple applications, such as localization, object tracking, mapping, and many more. Various solution paradigms have been proposed by the scientific community to solve this well established problem. Some of the commonly used techniques are based on Bayesian inference, specifically the particle filter as it has the advantage of modeling arbitrary distributions without the unimodal assumption limitation. The particle filter has proven to be successful in many applications, however, a large set of particles is required in order to have robust estimates against noisy measurements and erroneous data association, which impedes the runtime performance of the filter. This study shows that a learning framework that trains a recurrent neural network with labeled data generated from the probabilistic estimation of a particle filter is capable of exploiting the expressive power of neural networks in order to capture the behavior of the filter and handle the noisy sensory information. The trained model is capable of performing the estimation with lower runtime complexity, making it applicable to numerous autonomous systems. This approach also proves to be helpful in situations when the ground truth data can not be accessed. We train and evaluate our strategy using raw GPS sensor measurements from the Oxford RobotCar dataset. The results show that the performance of the recurrent network closely matches that of the particle filter without exhaustive tuning and that the network is able to generalize effectively on test datasets as well.